Question

What is the area of this figure? Enter your answer in the box. units² An irregular-shaped heptagon is graphed on a coordinate plane. The horizontal x-axis ranges from negative 6 to 6 in increments of 1. The vertical y-axis ranges from negative 6 to 6 in increments of 1. The vertices of the heptagon are located at begin ordered pair negative 3 comma 5 end ordered pair, begin ordered pair negative 1 comma 2 end ordered pair, begin ordered pair 1 comma 5 end ordered pair, begin ordered pair 3 comma 2 end ordered pair, begin ordered pair 3 comma negative 1 end ordered pair, begin ordered pair negative 5 comma negative 3 end ordered pair, and begin ordered pair negative 5 comma 2 end ordered pair.

Answer 1

I graphed the given points. A heptagon is a shape with seven sides. In the figure I graphed, I found familiar shapes like rectangle and triangles. I'll be using the formula of the triangle and rectangle when solving for its area.

Area of a triangle = (base * height) / 2
Area of a rectangle = length * width

I divided my graph into 3 parts. 1st part is the 2 triangles, 2nd part is the rectangle, 3rd part is the right triangle.

1st part
The 2 triangles each have a base of 4 units and a height of 3 units.
Area of a triangle = (base * height) / 2
A = (4 * 3)/2 = 12/2 = 6 square unit. per triangle.
Since there are 2 triangles, 6 sq.u * 2 = 12 sq.unit

2nd part
rectangle length = 8 units ; width = 3 units
Area of a rectangle = length * width = 8 * 3 = 24 sq. unit

3rd part
Right triangle: short leg = 2 units ; long leg = 8 units
Area of a right triangle = (long leg * short leg) / 2
Area of a right triangle = (8 * 2) / 2 = 16/2 = 8 sq. unit

Total area of the heptagon = 12 sq.u + 24 sq. u + 8 sq. u = 44 sq. unit.